Question

what is the magnitude of the gravitational force acting on a 79.5 - kg student due to a 58.0 - kg student sitting 2.40 m away in the classroom?
a. 7,850 n
b. 5.34×10^(-8) n
c. 7.91×10^(-10) n
d. 1.28×10^(-7) n
e. 6.29×10^(-8) n

Explanation:

Step1: Identify the formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.67\times10^{-11}\ N\cdot m^2/kg^2$, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Substitute the given values

Let $m_1 = 79.5\ kg$, $m_2 = 58.0\ kg$, and $r = 2.40\ m$. Then $F=6.67\times 10^{-11}\frac{79.5\times58.0}{(2.40)^2}$.
First, calculate the numerator: $79.5\times58.0 = 4611$.
Then, calculate the denominator: $(2.40)^2=5.76$.
So, $F = 6.67\times10^{-11}\times\frac{4611}{5.76}$.
$\frac{4611}{5.76}\approx800.52$.
$F = 6.67\times10^{-11}\times800.52$.
$F\approx5.34\times 10^{-8}\ N$.

Answer:

B. $5.34\times 10^{-8}\ N$